Geodesics算法在雷达投影转换中的应用检验

基于上海市气象局布设于临港的X波段移动式双线偏振雷达观测资料,利用反射率因子、差分反射率和相关系数等变量识别出东海大桥固定地物回波位置,进而采用Geodesics和HRAP(Hydrologic Rainfall Analysis Project)投影转换算法将雷达回波的极坐标位置转换至地理坐标。以国家测绘局利用GPS技术测量的沪芦高速(东海大桥段)地理坐标作为真值,将环境大气分为晴空回波-低湿度情况和降水回波-高湿度情况分类检验两种算法的效果。检验算法包含经投影转换后地物回波样本位于桥面主体内部的数目(多边形检验)和样本偏离桥体中心线的距离(中心线检验)。其结果表明:Geodesics算法在多边形和中心线检验方面表现均优于HRAP算法,其在雷达投影转换的实际业务中具备一定的应用价值。

The properties and geodesics related to the NUT-Taub-like spacetime

Some properties related to the NUT-Taub-like spacetime, such as the surface of infinite red-shift, horizon, singularity and the area of the NUT-Taub-like black hole are discussed. Furthermore, the geodesics in the NUT-Taub-like spacetime are obtained in some special cases. Specifically, the circular orbits for a massive particle are derived, which can reduce to the cases of the Schwarzschild spacetime and the NUT-Taub spacetime when m^＊ = 0 and m^＊ 〈〈 M, respectively.

Circular geodesics and accretion disk in the spacetime of a black hole including global monopole

We study circular time-like geodesics in the spacetime of a black hole including global monopole. We show that when the range of parameter changed the properties of the circular geodesics and the radiation of accretion disks are different. It follows that the properties of the accretion disk around black hole including global monopole can be different from that of a disk around Schwarzschild black hole.

Schwarzschild Geodesics in Terms of Elliptic Functions and the Related Red Shift

Using Weierstrassian elliptic functions the exact geodesics in the Schwarzschild metric are expressed in a simple and most transparent form. The results are useful for analytical and numerical applications. For example we calculate the perihelion precession and the light deflection in the post-Einsteinian approximation. The bounded orbits are computed in the post-Newtonian order. As a topical application we calculate the gravitational red shift for a star moving in the Schwarzschild field.

Null Geodesics, Raychaudhuri Equation, Trapped Surfaces, and Penrose Singularity Theorem

We review the concept of congruence of null geodesics, the Raychaudhuri equation for the expansion, its harmonic oscillator version and associated “quantum” propagator, the role of the equation in the derivation of the Penrose singularity theorem, the definition of trapped surfaces, and the derivation of the theorem itself.

MORSE CONCAVITY FOR CLOSED GEODESICS

In this paper, the concavity of closed geodesics proposed by M. Morse in 1930s is studied.

Null Geodesics in Brane World Scenarios

We study the null bulk geodesic motion in the brane world in which the bulk metric has an un-stabilized extra spatial dimension. We find that the null bulk geodesic motion as observed on the 3-brane with Z2 symmetry would be a timelike geodesic motion even though there exists an extra non-gravitational force in contrast with the case of the stabilized extra spatial dimension. In other words the presence of the extra non-gravitational force would not violate the Z2 symmetry.

An Implementation Method for the Geodesics with Constraints on Heisenberg Manifolds

In this paper we address the implementation issue of the geodesics method with constraints on Heisenberg manifolds. First we present more details on the method in order to facilitate its implementation and second we consider Mathema-tica as a software tool for the simulation. This implementation is of great importance since it allows easy and direct determination of Ricci tensor, which plays a fundamental role in the Heisenberg manifold metric.

Generic Existence of Infinitely Many Non-contractible Closed Geodesics on Compact Space Forms

Let M=S^(n)/Γand h be a nontrivial element of finite order p inπ_(1)(Μ),where the integers n,p≥2,Γis a finite abelian group which acts freely and isometrically on the n-sphere and therefore M is diffeomorphic to a compact space form.In this paper,we prove that there are infinitely many non-contractible closed geodesics of class[h]on the compact space form with C^(r)-generic Finsler metrics,where 4≤r≤∞.The conclusion also holds for Cr-generic Riemannian metrics for 2≤r≤∞.The proof is based on the resonance identity of non-contractible closed geodesics on compact space forms.

Principal Equatorial Null Geodesic Congruences in the Kerr Metric, and Their Quantum Propagators

Using the Raychaudhuri equation, we associate quantum probability amplitudes (propagators) to equatorial principal ingoing and outgoing null geodesic congruences in the Kerr metric. The expansion scalars diverge at the ring singularity;however, the propagators remain finite, which is an indication that at the quantum level singularities might disappear or, at least, become softened.

Morse index and the stability of closed geodesics

Let ind(c) be the Morse index of a closed geodesic c in an(n+1)-dimensional Riemannian manifold M.We prove that an oriented closed geodesic c is unstable if n + ind(c) is odd and a non-oriented closed geodesic c is unstable if n + ind(c) is even.Our result is a generalization of the famous theorem due to Poincar'e which states that the closed minimizing geodesic on a Riemann surface is unstable.

Some Remarks on the Geodesics in Infinite Dimensional Teichmuller Spaces

Let B denote the set of those points p in an infinite dimensional Teichmiiller space such that a geodesic between the zero point and p is not unique. Some properties of the set B are given.

On Nonuniqueness of Geodesics and Geodesic Disks in the Universal Asymptotic Teichmüller Space

Abstract The non-uniqueness on geodesics and geodesic disks in the universal asymptotic Teichmfiller space AT（D） are studied in this paper. It is proved that if # is asymptotically extremal in [[#]] with h （μ） 〈 h＊ （μ） for some point ζ∈D, then there exist infinitely many geodesic segments joining [[0]] and [[μ]], and infinitely many holomorphic geodesic disks containing [[0]] and [μ]] in AT（D）.

Geodesics in the Engel Group with a Sub-Lorentzian Metric——the Space-Like Case

Let E be the Engel group and D be a bracket generating left invariant distribution with a Lorentzian metric, which is a nondegenerate metric of index 1. In this paper, the author constructs a parametrization of a quasi-pendulum equation by Jacobi functions, and then gets the space-like Hamiltonian geodesics in the Engel group with a sub-Lorentzian metric.

On Unitary Invariant Weakly Complex Berwald Metrics with Vanishing Holomorphic Curvature and Closed Geodesics

In this paper, the authors construct a class of unitary invariant strongly pseudoconvex complex Finsler metrics which are of the form F =√[ rf(s- t)[, where r = ||v||~ 2, s =| z,v |~2/r, t =|| z||~ 2, f(w) is a real-valued smooth positive function of w ∈ R,and z is in a unitary invariant domain M C^n. Complex Finsler metrics of this form are unitary invariant. We prove that F is a class of weakly complex Berwald metrics whose holomorphic curvature and Ricci scalar curvature vanish identically and are independent of the choice of the function f. Under initial value conditions on f and its derivative f, we prove that all the real geodesics of F =√[rf(s- t)] on every Euclidean sphere S^(2n-1) M are great circles.

Nonholonomic Theory of Principal-direction Orthonormal Basis for a Layer of Surfaces

In order to carry out tensor analysis in a neighborhood of a reference surface,the principal-direction orthogonal basis accompanying with Lame s coefficients or general curvilinear coordinate systems are widely used.A novel kind of field theory termed as the nonholonomic theory of the Principal-Direction Orthonormal Basis(PDOB)is presented systematically in the present paper,in which the formal Christoffel symbols are related directly to the principal and geodesic curvatures with respect to the principal directions of the surface.Furthermore,a systematic and simple way to determine the curvatures of the surface are presented with some examples.It provides a way to recognize qualitatively the bending property of a surface.

Multiplicity of closed geodesics on Finsler spheres with irrationally elliptic closed geodesics

If all prime closed geodesics on(S^n, F) with an irreversible Finsler metric F are irrationally elliptic,there exist either exactly 2 [(n+1)/2] or infinitely many distinct closed geodesics. As an application, we show the existence of three distinct closed geodesics on bumpy Finsler(S^3, F) if any prime closed geodesic has non-zero Morse index.

凸复Finsler流形上的Hopf-Rinow定理

Suppose(M,F) is a convex complex Finsler manifold. We prove that geodesics of(M,F) are locally minimizing. Hence, F introduces a distance function d such that(M,d) is a metric space from topology. Next, we prove the classical Hopf-Rinow Theorem holds on(M,F).

Formation Mechanisms of Some Features in Siliceous Upper Cretaceous-Lower Tertiary Beds of Jordan-Undulations, Geodes, Boudinages

Geode, boudinage, and undulation structures are widely distributed in the siliceous beds of the Upper Cretaceous/Tertiary rocks in Jordan. Their formation was attributed to tectonic forces, syngenetic processes, organic disintegration processes, subaquatic gliding, compaction and settlement, and meteoritic impacts. In this work, the structural features in the siliceous beds of Jordan are attributed to an interplay of load and directed pressures, and mineralogical transformation processes (opal-A to opal-CT to quartz), governed by pH changes. Tectonic directed pressure was acting in an ESE-WSW direction and is common in the silicified limestone of Upper Cretaceous.

The Non-contractibility of Closed Geodesics on Finsler RP^(n)

Let(RP^(n),F)be a bumpy and irreversible Finsler n-dimensional real projective space with reversibilityλand flag curvature K satisfying(λ/1+λ)^(2)<K≤1 when n is odd,and K≥0 when n is even.We show that if there exist exactly 2[n+1/2]prime closed geodesics on such(RP^(n),F),then all of them are non-contractible,which coincides with the Katok’s examples.